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Compact block boundary value methods for semi‐linear delay‐reaction–diffusion equations with algebraic constraints
Author(s) -
Yan Xiaoqiang,
Zhang Chengjian
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22474
Subject(s) - mathematics , algebraic equation , block (permutation group theory) , boundary value problem , algebraic number , class (philosophy) , boundary (topology) , constraint (computer aided design) , order (exchange) , mathematical analysis , nonlinear system , geometry , computer science , physics , finance , quantum mechanics , artificial intelligence , economics
In the present paper, we study a class of linear approximation methods for solving semi‐linear delay‐reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth‐order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.